论文标题
在模块化不变的尖锐下限和分数dehn扭曲系数上
On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients
论文作者
论文摘要
曲线家族的模块化不变性是算术代数几何形状中的Arakelov不变性。这些不变的所有已知的均匀下限都不清晰。在本文中，我们的目的是给出曲线家族模块化不变的明确的下限，这对于第2属而言是鲜明的。根据分数Dehn Twist和模块化不变式之间的关系，我们给出了分数Dehn Twist系数的急剧下限，并对Pseudo-Periodic映射进行了pseudo-periodic映射，并具有最小的系数2和3级和3次和3次和3次和3次和3次和3次和3次和3。我们还为具有最小模块化不变的家庭和其他应用获得了僵化的特性。
Modular invariants of families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular invariants of families of curves, which is sharp for genus 2. According to the relation between fractional Dehn twists and modular invariants, we give the sharp lower bounds of fractional Dehn twist coefficients and classify pseudo-periodic maps with minimal coefficients for genus 2 and 3 firstly. We also obtain a rigidity property for families with minimal modular invariants, and other applications.
